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TrojanPoem

  • one year ago

Prove that : A, B, C > 0

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  1. TrojanPoem
    • one year ago
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    |dw:1434890770639:dw|

  2. TrojanPoem
    • one year ago
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    The value of the det is (A + B + C)^3

  3. dan815
    • one year ago
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    expand it

  4. TrojanPoem
    • one year ago
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    I found it's value with the tri method.

  5. TrojanPoem
    • one year ago
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    (A+B+C)^3

  6. dan815
    • one year ago
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    |dw:1434891229492:dw|

  7. TrojanPoem
    • one year ago
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    We have to prove that , The given is A , B, C > 0 so we can say their sum is also > 0 (A+B+C)^3 > 0

  8. TrojanPoem
    • one year ago
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    But expanding this A + B +c will take up to decade .

  9. dan815
    • one year ago
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    here is a method to show this is true

  10. TrojanPoem
    • one year ago
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    What's the method ?

  11. dan815
    • one year ago
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    lets say ABC are all approaching the same number,

  12. dan815
    • one year ago
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    |dw:1434891532175:dw|

  13. dan815
    • one year ago
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    now u were to begin varying B and C,

  14. dan815
    • one year ago
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    we can rewrite B and C as A-k

  15. dan815
    • one year ago
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    and lets Say we always make sure that A is always the biggest number or equal

  16. TrojanPoem
    • one year ago
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    So we will make assumption that A > b,c and b, c are approaching A

  17. TrojanPoem
    • one year ago
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    I have problem with electricity , I will re-log soon , sorry.

  18. dan815
    • one year ago
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    you can begin cancelling terms now

  19. dan815
    • one year ago
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    oh apparently there is a neat solution to this

  20. dan815
    • one year ago
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    |dw:1434892463880:dw|

  21. dan815
    • one year ago
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    for positive numbers

  22. dan815
    • one year ago
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    heres a proof for the binomial case, maybe u can spend some time to prove it for the trinomial

  23. dan815
    • one year ago
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    |dw:1434892832161:dw|

  24. TrojanPoem
    • one year ago
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    This is the arthmetic , geometric sequence inequality right ?

  25. TrojanPoem
    • one year ago
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    The Arithmetic mean is always greater than the geometric mean

  26. TrojanPoem
    • one year ago
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    But can you write the proof of this inequality ?

  27. dan815
    • one year ago
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    id have to work it out too,

  28. TrojanPoem
    • one year ago
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    Are you good with maxima and minima applications and complex number ?

  29. dan815
    • one year ago
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    sure : )

  30. TrojanPoem
    • one year ago
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    I will open a new question

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